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The recent discovery of a known infinite-dimensional algebra, w(1+infinity), among the asymptotic symmetries of four-dimensional asymptotically flat spacetimes has been interpreted as key evidence in support of a bottom-up approach to flat-space (a.k.a. celestial) holography.  In particular, since a holographic theory must realize the symmetries of its associated gravitational dual, large universal symmetries in principle impose fairly stringent constraints on a holographic correspondence. Of course, concrete progress relies crucially on the precise strength of the constraints from symmetry. Thus in pursuit of this larger goal, in this seminar, I will present a precise avatar of the universal  w(1+infinity) symmetry algebra that persists in the absence of gravity and in particular is realized in generic interacting four-dimensional conformal field theories.  The generators of the algebra are light-ray operators formed from null integrals of the stress tensor that generalize the average null energy operator.  I will discuss potential implications for conformal field theories in spacetime dimensions greater than two and celestial holography.